Integration

Question 1

How to integrate?

Answer 1

Opposite of differentiate
- Increase square number by 1
- Divide by that square number

e.g. 3x^2 = 3x^3/3 = x^3

Question 2

After every integration, what must u always add at the end?

Answer 2

• + C, cuz apparently we don;t know if we gat that or not so ya

Question 3

What’s integrals for?

Answer 3

Finding an area under a graph
- People who bored of the trapezium rule, so they were like “fuck it” and they made a super smart formula.

Question 4

How to use integrals? (calculator edition)

Answer 4

• u have the equation (3x^2 - x + 4)
• Top of f is a point in graph
• Bottom is same
• Ye just place everything as is in calculator

Tho formula we have is this:

b^f^a f(x) dx

(b at top, a at bottom)

Question 5

How to use integrals (not calculator edition)

Answer 5

• So u have the equation (3x^2 - x + 4)
• Integrate it (x^3 -x^2/2 + 4x)
• Ok and now u need the points for the certain area under graph:
  a = 1, b = 2
• Sub em in the integrated equation:
  For b = 2^3 - 2^2/2 + 4(2), For a = 1^3 - 1^2/2 + 4(1)
• And well, ye u minus them:
  b - a = area under graph
  Who knows what they equal? = 9.5

Question 6

Rq tips for integrals?

Answer 6

• Well first off, u’ll probably have to find the coordinates urself first, they give u equation of the curve so, ya gl.
• Might be simultaneous equations or just factorising type shi, woulda just said some e.g. but meh
• Additionally, be smart about it, cuz they’ll also tell u to find the area of shaded region.
• So in this case, u’ll probably have to either do 2 separate integrals, and minus them. OR, could just be a simple ass area of triangle, and minus n stuff.
• Really tho main thing, get ur points, use ur brain on integrals, and bam u got it.